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Secondary Hydrogen Isotope Effects on the Structure and Stability of Cation-π Complexes (Cation ) Li+, Na+, K+ and π ) Acetylene, Ethylene, Benzene) Diego V. Moreno, Sergio A. Gonza´lez, and Andre´s Reyes* Department of Chemistry, UniVersidad Nacional de Colombia, AV. Cra 30 45-03, Bogota´, Colombia ReceiVed: April 13, 2010; ReVised Manuscript ReceiVed: June 10, 2010
Secondary hydrogen isotope effects on the geometries, electronic wave functions and binding energies of cation-π complexes (cation ) Li+, Na+, K+ and π ) acetylene, ethylene, benzene) are investigated with NEO/HF and NEO/MP2 methods. These methods determine both electronic and nuclear wave functions simultaneously. Our results show that an increase of the hydrogen nuclear mass leads to the elongation of the cation-π bond distance and the decrease in its binding energy. An explanation to this behavior is given in terms of the changes in the π-molecule electronic structure and electrostatic potential induced by isotopic substitutions. 1. Introduction Cation-π interactions are recognized as strong noncovalent binding forces that play important roles in a wide variety of fields ranging from material design to molecular biology.1–4 Experimental data has shown that these interactions are unusually strong, with strengths similar to those of hydrogen bonds.2,5 The strength of cation-π interactions are determined by interactions forces between the cation and the π-system, that is, ion-dipole, ion-quadrupole, ion-induced dipole, chargetransfer, ane dispersion forces. However, a number of theoretical studies have concluded that these interactions are mainly electrostatic and dominated by the ion-quadupole interaction term. For instance, Kollman and co-workers6 showed in the Li+-ethylene complex that 60% of the binding is due to electrostatics. Dougherty et al.2 found a similar fraction for the Na+-benzene complex. Rodgers and co-workers7 found that electrostatic contributions to the binding are strongly influenced by substituents. In their work on cation-halobenzene complexes (cation ) Na+, K+; halogen ) F, Cl, Br, I), they observed that cation-π distances, RM⊥, gradually decreased and bond dissociation energies increased going from fluorine to iodine. They concluded that these trends arise form the electrostatic nature of the bonding and the inductive and polarization effects of the halogen substituent. An explanation of inductive substituent effects on the stability of cation-π interactions can be given in terms of changes in the polarization of π-system and direct through-space interactions with the substituent.8 Alternatively, a number of studies have demonstrated that the evaluation of the electrostatic potential (ESP) at a single point above the center of the substituted π-molecule can be used as a simple tool to predict the strength of the cation-π interaction; more negative ESPs indicate stronger interactions.8–10 To the best of our knowledge, there is neither experimental nor theoretical information available in the literature regarding secondary hydrogen isotope effects on the stability and structure of cation-π complexes. Experimental11 and theoretical12–16 studies have shown that the electronegativity of hydrogen isotopes increases with their mass. Therefore, it should be expected that the differences in electron-withdrawing strengths * To whom correspondence should be addressed. E-mail: areyesv@ unal.edu.co.
of hydrogen isotopes would have an impact on the electronic structure and electrostatic potential of π-molecules and, as a consequence, small effects on the binding energies and geometries of cation-π complexes. Different theoretical approaches are available now to study isotope effects on molecular systems. For example, conventional electronic structure (MO) calculations, based of the BornOppenheimer approximation (BOA), concentrate on the changes in zero-point energies (ZPE) to account for changes in stability. Effects on geometry, electronic structure, and electrostatic potential due to isotopic substitutions can be further incorporated considering corrections such as the diagonal correction to the BOA.14,17–21 Alternative approaches employing path integral molecular dynamics methods22–24 are capable of obtaining geometric isotope effects. However, these studies require the calculation of energies and forces via BOA methods; consequently, no changes in electronic structure due to isotopic substitutions can be observed. In recent years, several authors have proposed a variety of approaches beyond the BOA to study isotope and nuclear quantum effects (NQE) on the electronic structure and molecular geometries. Nakai25 recently presented an updated summary of these methodologies. Examples of these approaches are the multicomponent molecular orbital method (MCMO)26 proposed by Tachikawa and co-workers, the nuclear orbital molecular orbital method (NOMO)27 developed by Nakai and co-workers, the nuclear-electronic orbital approach (NEO)28 formulated by Hammes-Schiffer and co-workers, the any particle molecular orbital approach (APMO)29,30 implemented by Reyes and co-workers, among others. These nuclear molecular orbital (NMO) methods have been utilized successfully to study isotope effects on the electronic structure and geometry of small molecular systems and complexes.30–34 In the present work we investigate secondary H/D/T isotope effects on the structure and stability of prototype cation-π complexes (cation ) Li+, Na+, K+ and π ) acetylene, ethylene, benzene). Calculations are carried out at the NEO/HF and NEO/ MP2 levels of theory for both electrons and hydrogen nuclei. This paper is organized as follows: in Section 2 we summarize the details of the calculations. In Section 3 we study the isotope effects on the structure and wave functions of isolated π-molecules and the structure and stability of the cation-π complexes. Finally in Section 4 we provide some concluding remarks.
10.1021/jp103314p 2010 American Chemical Society Published on Web 08/12/2010
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TABLE 1: Optimized NEO/HF and NEO/MP2 Internuclear Distances (in Å) for C2X2, C2X4, and C6X6 (X ) H, D, T) NEO/HF
NEO/MP2
isotopologue
RC-C
RC-H
RC-C
C 2 H2 C 2 D2 C2T2 C2H2a C2H4 C 2 D4 C2T4 C2H4a C6H6 C 6 D6 C6T6 C6H6a
1.1847 1.1843 1.1841 1.1833 1.3195 1.3192 1.3191 1.3184 1.3871 1.3869 1.3867 1.3863
1.0578 1.0530 1.0509 1.0559 1.0829 1.0773 1.0749 1.0766 1.0816 1.0761 1.0737 1.0756
1.2169 1.2164 1.2162 1.2153 1.3386 1.3382 1.3381 1.3373 1.3988 1.3986 1.3984 1.3980
a
RC-H
Binding energies (Ebind) were evaluated with the expression
Exp. RC-C
Ebind ) Eπ · · · M - EM - Eπ
(1)
RC-H
1.0603 1.20341 1.06341 1.0573 1.0558 1.0653 1.0834 1.33942 1.08642 1.0796 1.0778 1.0848 1.0849 1.39742 1.08442 1.0810 1.0792 1.0861
where Eπ · · · M, EM, and Eπ are the optimized energies for the cation-π complex, the isolated cation (M+), and the π-molecule respectively. Calculated binding energies were also corrected for the electronic basis set superposition error (BSSE) via the standard counterpoise correction scheme.36 3. Results and Discussion 3.1. Isotope Effects on π-Molecules. To understand the nature of hydrogen isotope effects on cation-π complexes, we have first explored the hydrogen isotope effects on the geometries, energetics, and electronic wave functions of isolated π-molecules. Geometries. Table 1 summarizes NEO/HF and NEO/MP2 C-H (RC-H) and C-C (RC-C) internuclear distances for the hydrogen isotopologues of acetylene, ethylene, and benzene. Experimental data and conventional MO/HF, MO/MP2 results are also listed in that table. Figure 1 presents schematic illustrations of the π-molecules. As shown in Table 1, our NEO/MP2 RC-H and RC-C distances for all π-molecules are in good agreement with experiment. We observe that in all NEO calculations there is a progressive shortening of the RC-H distances with the gradual increase of the hydrogen mass. A similar trend has been obtained in other NMO studies on diatomic molecules.12,13,30 This behavior has been explained in terms of the anharmonicity of the potential experienced by the hydrogen nucleus and the inclusion of ZPE with the NMO method.12,13,32 We also notice a progressive shortening of the RC-C distance with the increase of the hydrogen mass. However, the magnitude of change in the RC-C distance is at least one order smaller than that of the RC-H distance. Energetics. Data presented in Table 2 reveal that NEO/HF and NEO/MP2 energies are higher than corresponding MO/HF and MO/MP2 energies. We anticipated these results because NEO/HF and NEO/MP2 total energies include not only the electronic but also the kinetic energy of the quantum nuclei. Electronic WaWe Functions. Isotope effects on electronic wave functions are analyzed in terms of changes in Mulliken and ChelpG partial atomic charges. NEO/HF and NEO/MP2 results for the π-molecule hydrogen isotopologues are reported in Table 2. In all cases, we notice that there are gradual
Conventional electronic structure calculation.
Figure 1. Schematic representation of the π-systems. (a) C2X2, (b) C2X4, (c) C6X6 (X ) H, D, T). Grids represent the hydrogen nuclei treated as quantum waves. Black balls represent carbon nuclei.
2. Computational Aspects All conventional Hartree-Fock (MO/HF), Møller-Plesset (MO/MP2), and NEO/HF calculations were performed with the GAMESS program.35 NEO/MP2 calculations were carried out with a modified version of GAMESS that fixes an error in the calculation of the second-order electron-nuclear correction to the energy. A 6-311++G(d,p) electronic basis set was utilized in all calculations. NEO/HF and NEO/MP2 calculations were carried out by treating hydrogen nuclei as quantum waves and lithium, carbon, sodium, and potassium nuclei as +3, +6, +11, and +19 point charges. A DZSPDN32 nuclear basis set was employed in all NEO calculations. We have set the tolerances for the SCF cycles and the energy gradient in the geometry optimization runs to 1 × 10-7 au. These tolerances will guarantee that the accuracy of the calculated differences in energies and geometries is better than the numerical error.
TABLE 2: NEO/HF and NEO/MP2 Total Energies (in au), Mulliken and ChelpG (in Parentheses) Partial Atomic Charges for the H/D/T Isotopologues of C2H2, C2H4, and C6H6 NEO/HF
NEO/MP2
partial charge
partial charge
isotopologue
total energy
C
H
total energy
C
C2H2 C 2 D2 C 2 T2 C2H2a C 2 H4 C 2 D4 C 2 T4 C2H4a C 6 H6 C 6 D6 C 6 T6 C6H6a
-76.7604 -76.7833 -76.7938 -76.8431 -77.8856 -77.9328 -77.9544 -78.0561 -230.5004 -230.5715 -230.6040 -230.7570
-0.3079 (-0.2709) -0.2942 (-0.2679) -0.2881 (-0.2666) -0.2619 (-0.2730) -0.2769 (-0.3052) -0.2598 (-0.3022) -0.2520 (-0.3011) -0.2216 (-0.3219) -0.2189 (-0.0891) -0.2089 (-0.0880) -0.2045 (-0.0876) -0.1850 (-0.0957)
0.3079 (0.2709) 0.2942 (0.2679) 0.2881 (0.2666) 0.2619 (0.2730) 0.1385 (0.1526) 0.1299 (0.1511) 0.1260 (0.1505) 0.1108 (0.1609) 0.2189 (0.0891) 0.2089 (0.0880) 0.2045 (0.0876) 0.1850 (0.0957)
-77.0755 -77.0967 -77.1066 -77.1537 -78.2268 -78.2707 -78.2910 -78.3881 -231.4689 -231.5347 -231.5651 -231.7109
-0.2699 (-0.2414) -0.2580 (-0.2393) -0.2525 (-0.2383) -0.2315 (-0.2741) -0.2775 (-0.2681) -0.2618 (-0.2672) -0.2547 (-0.2667) -0.2270 (-0.3488) -0.2035 (-0.0766) -0.1947 (-0.0762) -0.1908 (-0.0760) -0.1744 (-0.0903)
a
Conventional electronic structure calculation.
H 0.2699 (0.2414) 0.2580 0.2393) 0.2525 (0.2383) 0.2315 (0.2741) 0.1387 (0.1341) 0.1309 (0.1336) 0.1273 (0.1333) 0.1135 (0.1744) 0.2035 (0.0766) 0.1947 (0.0762) 0.1908 (0.0759) 0.1744 (0.0901)
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Figure 2. Schematic representation of cation-π complexes. (a) M+-C2X2, (b) M+-C2X4, (c) M+-C6X6 (X ) H, D, T). Grids represent the hydrogen nuclei treated as a quantum waves. Gold and black balls represent an alkali cation (Li+, Na+, K+) and carbon nuclei.
reductions in the negative partial charges on carbon atoms and the positive partial charges of hydrogen atoms as the mass of hydrogen becomes heavier. This inductive effect has been previously attributed to the increase of the electronegativity of the hydrogen isotopes with the nuclear mass.12–16 3.2. Isotope Effects on Cation-π Complexes. We now investigate the H/D/T isotope effects on the geometries, binding energies, and ESPs of cation-π complexes (cation ) Li+, Na+, K+; π ) acetylene, ethylene, benzene). Figure 2 shows schematic illustrations of these systems. Geometries. Table 3 summarizes NEO/HF and NEO/MP2 optimized internuclear RC-C, RC-H, and cation-π (RM ⊥) distances for the hydrogen isotopologues of the cation-π complexes. Conventional MO/HF and MO/MP2 distances are also presented in that table. To the best of our knowledge, there is no experimental information regarding the geometry of these complexes. Figure 2 presents schematic representations of the complexes. Results reported in Table 3 expose that a gradual increase of the hydrogen masses yields increases in the RM⊥ distances and reductions in the RC-H and RC-C distances. Surprisingly, changes in RM⊥ distances are of the same order of magnitude (1 × 10-3 Å) as those in the RC-H distances and are at least 1 order of magnitude larger than the changes in the
RC-C distances (1 × 10-4 Å). Although small, these isotope effects on the RC-H, RC-C, and RM⊥ distances are a clear manifestation of the nuclear quantum effects taken into account with the NMO methods. The lengthening of the M+-π distances with the increase in the hydrogen nuclear mass might be interpreted as a sign of the weakening of the M+-π bond. However, a more adequate estimation of the changes in the strength of cation-π interactions must be given in terms of binding energies. Binding Energies. Table 4 lists NEO/HF and NEO/MP2 binding energies for the hydrogen isotopologues of the cation-π complexes. MO/HF and MO/MP2 results are also included in that table. Clear trends emerge regardless of the NEO level of theory. For instance, binding energies of cation-π complexes decrease when the hydrogen mass becomes heavier. Results with conventional MO/HF and MO/MP2, where mass of the hydrogen is taken as infinite, also follow the NEO energy trends (in MO T D H absolute value), that is, Ebind < Ebind < Ebind < Ebind . Besides, considering that the electronegativity of a hydrogen isotope increases with its mass, this might suggest that the binding energy of cation-π complex isotopologues decrease with the increase of the electronegativity of the hydrogen isotope. To further confirm that isotope effects on the binding energies of cation-π complexes are of inductive nature, we employ the two electrostatic models proposed by Mecozzi et al.9 in which variations in the binding energies are rationalized in terms of variations in the ESPs. Electrostatic Potentials and Binding Energies. In the first model, the cation at its optimized position is replaced with a dummy probe atom and the ESP is evaluated at that point (ESPs calculated using this model will be referred as ESPopt throughout). In the second model, the calculation of the ESP is performed using the geometry of the uncomplexed π-molecules, at a distance above the center of the molecular plane corre-
TABLE 3: NEO/HF and NEO/MP2 Equilibrium Internuclear Distances (in Å) for the M+-π Complexes NEO/HF Li
+
Na+
K+
+
RC-C
RC-H
RLi+⊥
RC-C
RC-H
RNa+⊥
RC-C
RC-H
RK+⊥
+
M -C2H2 M+-C2D2 M+-C2T2 M+-C2H2a M+-C2H4 M+-C2D4 M+-C2T4 M+-C2H4a M+-C6H6 M+-C6D6 M+-C6T6 M+-C6H6a
1.1902 1.1898 1.1896 1.1888 1.3321 1.3317 1.3315 1.3308 1.3948 1.3945 1.3944 1.3938
1.0657 1.0604 1.0581 1.0626 1.0852 1.0794 1.0769 1.0786 1.0806 1.0749 1.0724 1.0747
2.2416 2.2445 2.2458 2.2513 2.3023 2.3061 2.3078 2.3153 1.8802 1.8826 1.8837 1.8886
1.1888 1.1884 1.1882 1.1873 1.3290 1.3286 1.3285 1.3276 1.3929 1.3926 1.3924 1.3919
1.0636 1.0584 1.0561 1.0608 1.0845 1.0788 1.0763 1.0781 1.0811 1.0755 1.0730 1.0752
2.6769 2.6803 2.6818 2.6885 2.7237 2.7280 2.7299 2.7383 2.4669 2.4699 2.4712 2.4775
1.1872 1.1868 1.1866 1.1857 1.3252 1.3248 1.3247 1.3239 1.3912 1.3909 1.3908 1.3902
1.0619 1.0568 1.0546 1.0594 1.0841 1.0784 1.0759 1.0777 1.0814 1.0758 1.0734 1.0755
3.2111 3.2157 3.2178 3.2267 3.2798 3.2849 3.2871 3.2973 2.9882 2.9922 2.9939 3.0022
M+-C2H2 M+-C2D2 M+-C2T2 M+-C2H2a M+-C2H4 M+-C2D4 M+-C2T4 M+-C2H4a M+-C6H6 M+-C6D6 M+-C6T6 M+-C6H6a
1.2224 1.2219 1.2217 1.2208 1.3498 1.3494 1.3492 1.3483 1.4071 1.4068 1.4066 1.4060
1.0659 1.0636 1.0623 1.0726 1.0864 1.0824 1.0806 1.0877 1.0839 1.0800 1.0782 1.0858
2.2115 2.2143 2.2155 2.2211 2.2569 2.2610 2.2628 2.2709 1.8390 1.8415 1.8426 1.8479
NEO/MP2 1.2212 1.2207 1.2205 1.2195 1.3473 1.3468 1.3466 1.3457 1.4051 1.4047 1.4046 1.4040
1.0639 1.0616 1.0604 1.0708 1.0856 1.0817 1.0798 1.0869 1.0845 1.0805 1.0787 1.0862
2.6205 2.6237 2.6251 2.6315 2.6568 2.6613 2.6633 2.6720 2.3917 2.3946 2.3959 2.4020
1.2197 1.2193 1.2191 1.2181 1.3441 1.3437 1.3435 1.3426 1.4031 1.4028 1.4027 1.4021
1.0624 1.0602 1.0590 1.0694 1.0849 1.0810 1.0792 1.0863 1.0847 1.0808 1.0790 1.0864
3.0537 3.0574 3.0591 3.0665 3.1097 3.1144 3.1164 3.1260 2.7942 2.7974 2.7987 2.8125
M complex
a
Conventional electronic structure calculation.
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TABLE 4: NEO/HF and NEO/MP2M+-π Binding Energies (BSSE Corrected Energies in Parentheses) (in kcal/mol) NEO/HF M
+
M+-C2H2 M+-C2D2 M+-C2T2 M+-C2H2a M+-C2H4 M+-C2D4 M+-C2T4 M+-C2H4a M+-C6H6 M+-C6D6 M+-C6T6 M+-C6H6a a
Li
+
21.44(21.35) 21.12(21.04) 20.99(20.90) 20.39(20.31) 22.13(22.03) 21.79(21.70) 21.65(21.56) 21.00(20.92) 40.00(39.64) 39.51(39.16) 39.31(38.96) 38.33(38.00)
Na
NEO/MP2
+
13.23(13.12) 13.01(12.90) 12.91(12.49) 12.48(12.37) 13.99(13.86) 13.75(13.63) 13.65(13.53) 13.18(13.06) 24.59(24.15) 24.22(23.79) 24.06(23.63) 23.32(22.92)
K
+
Li
7.65(7.58) 7.49(7.43) 7.42(7.36) 7.13(7.07) 8.09(8.03) 7.93(7.87) 7.86(7.80) 7.54(7.49) 16.63(16.42) 16.34(16.13) 16.22(16.01) 15.64(15.44)
+
22.10(20.20) 21.78(19.90) 21.64(19.77) 21.02(19.18) 22.31(20.70) 21.97(20.39) 21.81(20.26) 21.13(19.63) 41.46(36.86) 40.99(36.43) 40.78(36.24) 39.65(35.19)
Na+
K+
14.08(12.49) 13.85(12.28) 13.74(12.18) 13.29(11.76) 14.49(13.13) 14.24(12.91) 14.13(12.81) 13.63(12.36) 26.33(22.57) 25.97(22.24) 25.81(22.10) 24.91(21.28)
9.17(8.09) 9.00(7.94) 8.93(7.87) 8.60(7.56) 9.55(8.58) 9.37(8.42) 9.37(8.35) 8.94(8.02) 20.73(17.80) 20.43(17.52) 20.30(17.40) 19.55(16.77)
Conventional electronic structure calculation.
Figure 3. NEO/HF binding energies for M+-π complexes vs electrostatic potentials (calculated using the first model). Solid lines and circle markers for M+-C2H4, dashed line and square markers for M+-C2H2, and dash-dot lines and diamond markers for M+-C6H6.
Figure 4. NEO/MP2 binding energies for M+-π complexes vs electrostatic potential (calculated using the first model). Solid line and circle markers for M+-C2H4, dashed lines and square markers for M+-C2H2, and dash-dot line and diamond markers for M+-C6H6.
sponding to the equilibrium bond distances with each cation (ESPs calculated using this model will be referred as ESPunopt throughout). In both models, the ESPs are plotted versus the binding energies. Linearity of the plots demonstrate the electrostatic nature of the cation-π interaction. According to Mecozzi et al., either model should lead to the same conclusions. First model: In Figures 3 and 4 we plotted NEO/HF binding energies versus ESPopt. In these plots we have also included MO/HF results, which are the limit of infinite mass for hydrogen nuclei in a NMO/HF method.31,37 Except for the Li+-benzene, all the complexes presented good correlations (r > 0.925).
In Figure 4, we plotted NEO/MP2 Ebind versus ESPopt. Except for Li+-benzene, all plots show excellent correlations (r > 0.99). This time MO/MP2 results were not included in the plots, because otherwise the correlation would be lost. Contrary to MO/HF ESPs, MO/MP2 ESPs do not necessarily follow the same trends of NEO/MP2 ESPs with the increase of the hydrogen nuclear mass. This is a consequence of the fact that changes in zero-order wave functions, nuclear delocalization and nuclear-electron correlation do not necessarily follow the same trends with increasing masses.30 Second model: In Figures 5 and 6 we plotted NEO/HF and NEO/MP2 Ebind versus ESPunopt. Surprisingly, except for
Secondary Hydrogen Isotope Effects
Figure 5. NEO/HF binding energies for M+-π complexes vs electrostatic potential (calculated using the second model). Solid lines and circle markers for M+-C2H4, dashed line and square markers for M+-C2H2, and dash-dot line and diamond markers for M+-C6H6.
K+-C2H2 (r ) 0.9403) and K+-C2H4 (r ) 0.9523) all systems show excellent correlations (r > 0.9999). The results presented so far using these models (except for Li+-C6H6 in the first model) reveal that there is a direct relation between the electronegativities of the hydrogen isotopes and the binding energies. These trends in electronegativities are similar to those reported by Rodgers for halobenzenes.7 To further investigate if these trends in electronegativity still hold for halogenated acetylene (C2X2) and ethylene (C2X4) (X ) F, Cl, Br), we calculated at the MO/HF and MO/MP2 levels the equilibrium geometries and energies of C2X2, C2X4, Li+-C2X2, and Li+-C2X4. In Table 5 we reported RM⊥ distances and the binding energies. ESPs calculated with the second model are also included in that table. We clearly observe that an increase in the electronegativity of the substituents results in the elongation and weakening of the M+-π bond as well as the reduction in the negative ESPs. These trends in the electronegativities of halogen substituents are completely consistent with the trends we obtained for the hydrogen isotopologues of the cation-π complexes. Our results confirm for the first time using a NMO method the inductive nature of the isotope effects on the stability and structure of cation-π systems. A further analysis in terms of the Morokuma-Kitaura energy decomposition scheme for HF38,39 or the symmetry-adapted perturbation theory (SAPT)40 will help us to elucidate in detail the nature of these isotope effects on the cation-π interaction. We are currently working on extensions of these schemes at the NMO level.
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Figure 6. NEO/MP2 binding energies for M+-π complexes vs electrostatic potential (calculated using the second model). Solid lines and circle markers for M+-C2H4, dashed lines and square markers for M+-C2H2, and dash-dot line and diamond markers for M+-C6H6.
TABLE 5: MO/HF and MO/MP2 Li+-C2Y2 and Li+-C2Y4 (Y ) F, Cl, Br) Equilibrium RLi+⊥ Distances (in Å), E bind (in kcal/mol), and Electrostatic Potentials (in kcal/mol)
+
Li -C2Br2 Li+-C2Cl2 Li+-C2F2 Li+-C2Br4 Li+-C2Cl4 Li+-C2F4
RLi+⊥
MO/HF Ebind
ESP
RLi+⊥
MO/MP2 Ebind
ESP
2.2289 2.2676 2.3909 2.3012 2.3603 2.6774
18.20 14.88 7.36 13.67 9.18 0.16
-6.72 -4.76 0.12 3.35 5.08 8.41
2.1632 2.1958 2.3359 2.1567 2.1883 2.5351
22.25 19.10 9.37 21.45 17.01 2.16
-7.2 -5.61 -0.01 1.69 3.62 8.21
4. Conclusions NEO/HF and NEO/MP2 calculations were performed to study H/D/T isotope effects on the binding energies and M+-π bond distances of cation-π complexes. Our calculations show that a gradual increase of the hydrogen mass leads to the destabilization and elongation of the M+-π bond. Two electrostatic models have permitted us to demonstrate the inductive nature of these isotope effects. To our knowledge these are the first NMO calculations that expose the importance of inductive isotope effects on noncovalent interactions. This study also reveals the potential of NMO methods for more thorough studies of secondary isotope effects. Acknowledgment. The authors wish to thank Universidad Nacional for the financial support (DIB projects 201010011893 and 201010013258).
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